Is the simulated data generally on the same scale as the outcome?
Useful for working through new techniques
[1] 15.052024 10.516033 48.768134 6.051757 23.568834 8.215073 8.358373
[8] 10.965030 18.721478 6.185453 33.463990 7.692346 8.183408 38.299289
[15] 19.662011 40.735673 47.761948 8.941139 14.348609 17.649784 10.298022
[22] 16.744447 18.485528 4.401309 20.393710 9.387616 18.634552 3.833338
[29] 12.991330 14.447092 10.030150 34.974844 5.855171 13.695729 6.122422
[36] 7.711018 15.457268 12.589072 23.771346 13.454850 16.433005 7.669530
[43] 7.016928 10.147020 10.392751 14.755238 5.863227 11.664974 37.834532
[50] 8.122134 11.637684 8.054722 10.671032 11.067064 19.764847 11.350978
[57] 5.528933 11.334868 10.751546 7.264224 11.535853 7.576272 38.627318
[64] 8.357703 17.193855 12.844281 14.871730 23.751698 19.244272 15.178204
[71] 25.143548 9.448907 5.198409 18.509202 6.271502 4.401013 8.829788
[78] 3.829214 20.244310 7.092822 15.633127 7.137421 15.143549 8.846810
[85] 11.810036 19.420051 14.109783 12.172618 20.902973 16.982590 14.497679
[92] 8.214659 23.667628 11.506670 10.022089 8.371849 11.861825 6.422960
[99] 28.380817 12.254432
\[DBH \sim Normal(\mu, \sigma)\]
mean and sd are drawn from distributions themselvestruncnorm::rtruncnorm() to generate a half-normal distributiona = 0 sets the lower bound at 0# A tibble: 2,000 × 2
ID DBH
<int> <dbl>
1 1 8.37
2 1 7.83
3 1 13.0
4 1 10.7
5 1 18.4
6 1 10.3
7 1 10.4
8 1 12.1
9 1 11.4
10 1 13.4
# … with 1,990 more rows
\[DBH \sim LogNormal(\mu, \sigma)\]
\[\mu \sim Normal(3, 0.2)\] \[\sigma \sim HalfNormal(1, 0.25)\]
rethinking::ulam() converts model statements to stan code and samples the model.
Running MCMC with 4 parallel chains, with 1 thread(s) per chain...
Chain 1 Iteration: 1 / 5000 [ 0%] (Warmup)
Chain 1 Iteration: 100 / 5000 [ 2%] (Warmup)
Chain 1 Iteration: 200 / 5000 [ 4%] (Warmup)
Chain 1 Iteration: 300 / 5000 [ 6%] (Warmup)
Chain 1 Iteration: 400 / 5000 [ 8%] (Warmup)
Chain 1 Iteration: 500 / 5000 [ 10%] (Warmup)
Chain 1 Iteration: 600 / 5000 [ 12%] (Warmup)
Chain 1 Iteration: 700 / 5000 [ 14%] (Warmup)
Chain 1 Iteration: 800 / 5000 [ 16%] (Warmup)
Chain 1 Iteration: 900 / 5000 [ 18%] (Warmup)
Chain 1 Iteration: 1000 / 5000 [ 20%] (Warmup)
Chain 1 Iteration: 1100 / 5000 [ 22%] (Warmup)
Chain 1 Iteration: 1200 / 5000 [ 24%] (Warmup)
Chain 1 Iteration: 1300 / 5000 [ 26%] (Warmup)
Chain 1 Iteration: 1400 / 5000 [ 28%] (Warmup)
Chain 1 Iteration: 1500 / 5000 [ 30%] (Warmup)
Chain 1 Iteration: 1600 / 5000 [ 32%] (Warmup)
Chain 1 Iteration: 1700 / 5000 [ 34%] (Warmup)
Chain 1 Iteration: 1800 / 5000 [ 36%] (Warmup)
Chain 1 Iteration: 1900 / 5000 [ 38%] (Warmup)
Chain 1 Iteration: 2000 / 5000 [ 40%] (Warmup)
Chain 1 Iteration: 2100 / 5000 [ 42%] (Warmup)
Chain 1 Iteration: 2200 / 5000 [ 44%] (Warmup)
Chain 1 Iteration: 2300 / 5000 [ 46%] (Warmup)
Chain 1 Iteration: 2400 / 5000 [ 48%] (Warmup)
Chain 1 Iteration: 2500 / 5000 [ 50%] (Warmup)
Chain 1 Iteration: 2501 / 5000 [ 50%] (Sampling)
Chain 1 Iteration: 2600 / 5000 [ 52%] (Sampling)
Chain 1 Iteration: 2700 / 5000 [ 54%] (Sampling)
Chain 1 Iteration: 2800 / 5000 [ 56%] (Sampling)
Chain 1 Iteration: 2900 / 5000 [ 58%] (Sampling)
Chain 1 Iteration: 3000 / 5000 [ 60%] (Sampling)
Chain 1 Iteration: 3100 / 5000 [ 62%] (Sampling)
Chain 1 Iteration: 3200 / 5000 [ 64%] (Sampling)
Chain 1 Iteration: 3300 / 5000 [ 66%] (Sampling)
Chain 1 Iteration: 3400 / 5000 [ 68%] (Sampling)
Chain 1 Iteration: 3500 / 5000 [ 70%] (Sampling)
Chain 1 Iteration: 3600 / 5000 [ 72%] (Sampling)
Chain 1 Iteration: 3700 / 5000 [ 74%] (Sampling)
Chain 1 Iteration: 3800 / 5000 [ 76%] (Sampling)
Chain 1 Iteration: 3900 / 5000 [ 78%] (Sampling)
Chain 1 Iteration: 4000 / 5000 [ 80%] (Sampling)
Chain 1 Iteration: 4100 / 5000 [ 82%] (Sampling)
Chain 1 Iteration: 4200 / 5000 [ 84%] (Sampling)
Chain 1 Iteration: 4300 / 5000 [ 86%] (Sampling)
Chain 1 Iteration: 4400 / 5000 [ 88%] (Sampling)
Chain 1 Iteration: 4500 / 5000 [ 90%] (Sampling)
Chain 1 Iteration: 4600 / 5000 [ 92%] (Sampling)
Chain 1 Iteration: 4700 / 5000 [ 94%] (Sampling)
Chain 1 Iteration: 4800 / 5000 [ 96%] (Sampling)
Chain 1 Iteration: 4900 / 5000 [ 98%] (Sampling)
Chain 1 Iteration: 5000 / 5000 [100%] (Sampling)
Chain 2 Iteration: 1 / 5000 [ 0%] (Warmup)
Chain 2 Iteration: 100 / 5000 [ 2%] (Warmup)
Chain 2 Iteration: 200 / 5000 [ 4%] (Warmup)
Chain 2 Iteration: 300 / 5000 [ 6%] (Warmup)
Chain 2 Iteration: 400 / 5000 [ 8%] (Warmup)
Chain 2 Iteration: 500 / 5000 [ 10%] (Warmup)
Chain 2 Iteration: 600 / 5000 [ 12%] (Warmup)
Chain 2 Iteration: 700 / 5000 [ 14%] (Warmup)
Chain 2 Iteration: 800 / 5000 [ 16%] (Warmup)
Chain 2 Iteration: 900 / 5000 [ 18%] (Warmup)
Chain 2 Iteration: 1000 / 5000 [ 20%] (Warmup)
Chain 2 Iteration: 1100 / 5000 [ 22%] (Warmup)
Chain 2 Iteration: 1200 / 5000 [ 24%] (Warmup)
Chain 2 Iteration: 1300 / 5000 [ 26%] (Warmup)
Chain 2 Iteration: 1400 / 5000 [ 28%] (Warmup)
Chain 2 Iteration: 1500 / 5000 [ 30%] (Warmup)
Chain 2 Iteration: 1600 / 5000 [ 32%] (Warmup)
Chain 2 Iteration: 1700 / 5000 [ 34%] (Warmup)
Chain 2 Iteration: 1800 / 5000 [ 36%] (Warmup)
Chain 2 Iteration: 1900 / 5000 [ 38%] (Warmup)
Chain 2 Iteration: 2000 / 5000 [ 40%] (Warmup)
Chain 2 Iteration: 2100 / 5000 [ 42%] (Warmup)
Chain 2 Iteration: 2200 / 5000 [ 44%] (Warmup)
Chain 2 Iteration: 2300 / 5000 [ 46%] (Warmup)
Chain 2 Iteration: 2400 / 5000 [ 48%] (Warmup)
Chain 2 Iteration: 2500 / 5000 [ 50%] (Warmup)
Chain 2 Iteration: 2501 / 5000 [ 50%] (Sampling)
Chain 2 Iteration: 2600 / 5000 [ 52%] (Sampling)
Chain 2 Iteration: 2700 / 5000 [ 54%] (Sampling)
Chain 2 Iteration: 2800 / 5000 [ 56%] (Sampling)
Chain 2 Iteration: 2900 / 5000 [ 58%] (Sampling)
Chain 2 Iteration: 3000 / 5000 [ 60%] (Sampling)
Chain 2 Iteration: 3100 / 5000 [ 62%] (Sampling)
Chain 2 Iteration: 3200 / 5000 [ 64%] (Sampling)
Chain 2 Iteration: 3300 / 5000 [ 66%] (Sampling)
Chain 2 Iteration: 3400 / 5000 [ 68%] (Sampling)
Chain 2 Iteration: 3500 / 5000 [ 70%] (Sampling)
Chain 2 Iteration: 3600 / 5000 [ 72%] (Sampling)
Chain 2 Iteration: 3700 / 5000 [ 74%] (Sampling)
Chain 2 Iteration: 3800 / 5000 [ 76%] (Sampling)
Chain 2 Iteration: 3900 / 5000 [ 78%] (Sampling)
Chain 2 Iteration: 4000 / 5000 [ 80%] (Sampling)
Chain 2 Iteration: 4100 / 5000 [ 82%] (Sampling)
Chain 2 Iteration: 4200 / 5000 [ 84%] (Sampling)
Chain 2 Iteration: 4300 / 5000 [ 86%] (Sampling)
Chain 2 Iteration: 4400 / 5000 [ 88%] (Sampling)
Chain 2 Iteration: 4500 / 5000 [ 90%] (Sampling)
Chain 2 Iteration: 4600 / 5000 [ 92%] (Sampling)
Chain 2 Iteration: 4700 / 5000 [ 94%] (Sampling)
Chain 2 Iteration: 4800 / 5000 [ 96%] (Sampling)
Chain 2 Iteration: 4900 / 5000 [ 98%] (Sampling)
Chain 2 Iteration: 5000 / 5000 [100%] (Sampling)
Chain 3 Iteration: 1 / 5000 [ 0%] (Warmup)
Chain 3 Iteration: 100 / 5000 [ 2%] (Warmup)
Chain 3 Iteration: 200 / 5000 [ 4%] (Warmup)
Chain 3 Iteration: 300 / 5000 [ 6%] (Warmup)
Chain 3 Iteration: 400 / 5000 [ 8%] (Warmup)
Chain 3 Iteration: 500 / 5000 [ 10%] (Warmup)
Chain 3 Iteration: 600 / 5000 [ 12%] (Warmup)
Chain 3 Iteration: 700 / 5000 [ 14%] (Warmup)
Chain 3 Iteration: 800 / 5000 [ 16%] (Warmup)
Chain 3 Iteration: 900 / 5000 [ 18%] (Warmup)
Chain 3 Iteration: 1000 / 5000 [ 20%] (Warmup)
Chain 3 Iteration: 1100 / 5000 [ 22%] (Warmup)
Chain 3 Iteration: 1200 / 5000 [ 24%] (Warmup)
Chain 3 Iteration: 1300 / 5000 [ 26%] (Warmup)
Chain 3 Iteration: 1400 / 5000 [ 28%] (Warmup)
Chain 3 Iteration: 1500 / 5000 [ 30%] (Warmup)
Chain 3 Iteration: 1600 / 5000 [ 32%] (Warmup)
Chain 3 Iteration: 1700 / 5000 [ 34%] (Warmup)
Chain 3 Iteration: 1800 / 5000 [ 36%] (Warmup)
Chain 3 Iteration: 1900 / 5000 [ 38%] (Warmup)
Chain 3 Iteration: 2000 / 5000 [ 40%] (Warmup)
Chain 3 Iteration: 2100 / 5000 [ 42%] (Warmup)
Chain 3 Iteration: 2200 / 5000 [ 44%] (Warmup)
Chain 3 Iteration: 2300 / 5000 [ 46%] (Warmup)
Chain 3 Iteration: 2400 / 5000 [ 48%] (Warmup)
Chain 3 Iteration: 2500 / 5000 [ 50%] (Warmup)
Chain 3 Iteration: 2501 / 5000 [ 50%] (Sampling)
Chain 3 Iteration: 2600 / 5000 [ 52%] (Sampling)
Chain 3 Iteration: 2700 / 5000 [ 54%] (Sampling)
Chain 3 Iteration: 2800 / 5000 [ 56%] (Sampling)
Chain 3 Iteration: 2900 / 5000 [ 58%] (Sampling)
Chain 3 Iteration: 3000 / 5000 [ 60%] (Sampling)
Chain 3 Iteration: 3100 / 5000 [ 62%] (Sampling)
Chain 3 Iteration: 3200 / 5000 [ 64%] (Sampling)
Chain 3 Iteration: 3300 / 5000 [ 66%] (Sampling)
Chain 3 Iteration: 3400 / 5000 [ 68%] (Sampling)
Chain 3 Iteration: 3500 / 5000 [ 70%] (Sampling)
Chain 3 Iteration: 3600 / 5000 [ 72%] (Sampling)
Chain 3 Iteration: 3700 / 5000 [ 74%] (Sampling)
Chain 3 Iteration: 3800 / 5000 [ 76%] (Sampling)
Chain 3 Iteration: 3900 / 5000 [ 78%] (Sampling)
Chain 3 Iteration: 4000 / 5000 [ 80%] (Sampling)
Chain 3 Iteration: 4100 / 5000 [ 82%] (Sampling)
Chain 3 Iteration: 4200 / 5000 [ 84%] (Sampling)
Chain 3 Iteration: 4300 / 5000 [ 86%] (Sampling)
Chain 3 Iteration: 4400 / 5000 [ 88%] (Sampling)
Chain 3 Iteration: 4500 / 5000 [ 90%] (Sampling)
Chain 3 Iteration: 4600 / 5000 [ 92%] (Sampling)
Chain 3 Iteration: 4700 / 5000 [ 94%] (Sampling)
Chain 3 Iteration: 4800 / 5000 [ 96%] (Sampling)
Chain 3 Iteration: 4900 / 5000 [ 98%] (Sampling)
Chain 3 Iteration: 5000 / 5000 [100%] (Sampling)
Chain 4 Iteration: 1 / 5000 [ 0%] (Warmup)
Chain 4 Iteration: 100 / 5000 [ 2%] (Warmup)
Chain 4 Iteration: 200 / 5000 [ 4%] (Warmup)
Chain 4 Iteration: 300 / 5000 [ 6%] (Warmup)
Chain 4 Iteration: 400 / 5000 [ 8%] (Warmup)
Chain 4 Iteration: 500 / 5000 [ 10%] (Warmup)
Chain 4 Iteration: 600 / 5000 [ 12%] (Warmup)
Chain 4 Iteration: 700 / 5000 [ 14%] (Warmup)
Chain 4 Iteration: 800 / 5000 [ 16%] (Warmup)
Chain 4 Iteration: 900 / 5000 [ 18%] (Warmup)
Chain 4 Iteration: 1000 / 5000 [ 20%] (Warmup)
Chain 4 Iteration: 1100 / 5000 [ 22%] (Warmup)
Chain 4 Iteration: 1200 / 5000 [ 24%] (Warmup)
Chain 4 Iteration: 1300 / 5000 [ 26%] (Warmup)
Chain 4 Iteration: 1400 / 5000 [ 28%] (Warmup)
Chain 4 Iteration: 1500 / 5000 [ 30%] (Warmup)
Chain 4 Iteration: 1600 / 5000 [ 32%] (Warmup)
Chain 4 Iteration: 1700 / 5000 [ 34%] (Warmup)
Chain 4 Iteration: 1800 / 5000 [ 36%] (Warmup)
Chain 4 Iteration: 1900 / 5000 [ 38%] (Warmup)
Chain 4 Iteration: 2000 / 5000 [ 40%] (Warmup)
Chain 4 Iteration: 2100 / 5000 [ 42%] (Warmup)
Chain 4 Iteration: 2200 / 5000 [ 44%] (Warmup)
Chain 4 Iteration: 2300 / 5000 [ 46%] (Warmup)
Chain 4 Iteration: 2400 / 5000 [ 48%] (Warmup)
Chain 4 Iteration: 2500 / 5000 [ 50%] (Warmup)
Chain 4 Iteration: 2501 / 5000 [ 50%] (Sampling)
Chain 4 Iteration: 2600 / 5000 [ 52%] (Sampling)
Chain 4 Iteration: 2700 / 5000 [ 54%] (Sampling)
Chain 4 Iteration: 2800 / 5000 [ 56%] (Sampling)
Chain 4 Iteration: 2900 / 5000 [ 58%] (Sampling)
Chain 4 Iteration: 3000 / 5000 [ 60%] (Sampling)
Chain 4 Iteration: 3100 / 5000 [ 62%] (Sampling)
Chain 4 Iteration: 3200 / 5000 [ 64%] (Sampling)
Chain 4 Iteration: 3300 / 5000 [ 66%] (Sampling)
Chain 4 Iteration: 3400 / 5000 [ 68%] (Sampling)
Chain 4 Iteration: 3500 / 5000 [ 70%] (Sampling)
Chain 4 Iteration: 3600 / 5000 [ 72%] (Sampling)
Chain 4 Iteration: 3700 / 5000 [ 74%] (Sampling)
Chain 4 Iteration: 3800 / 5000 [ 76%] (Sampling)
Chain 4 Iteration: 3900 / 5000 [ 78%] (Sampling)
Chain 4 Iteration: 4000 / 5000 [ 80%] (Sampling)
Chain 4 Iteration: 4100 / 5000 [ 82%] (Sampling)
Chain 4 Iteration: 4200 / 5000 [ 84%] (Sampling)
Chain 4 Iteration: 4300 / 5000 [ 86%] (Sampling)
Chain 4 Iteration: 4400 / 5000 [ 88%] (Sampling)
Chain 4 Iteration: 4500 / 5000 [ 90%] (Sampling)
Chain 4 Iteration: 4600 / 5000 [ 92%] (Sampling)
Chain 4 Iteration: 4700 / 5000 [ 94%] (Sampling)
Chain 4 Iteration: 4800 / 5000 [ 96%] (Sampling)
Chain 4 Iteration: 4900 / 5000 [ 98%] (Sampling)
Chain 4 Iteration: 5000 / 5000 [100%] (Sampling)
Chain 1 finished in 0.1 seconds.
Chain 2 finished in 0.1 seconds.
Chain 3 finished in 0.1 seconds.
Chain 4 finished in 0.1 seconds.
All 4 chains finished successfully.
Mean chain execution time: 0.1 seconds.
Total execution time: 0.3 seconds.
Inference for Stan model: ulam_cmdstanr_2c9c44adfe28e9c6b44eeb19d995e263-202302200926-1-595662.
4 chains, each with iter=5000; warmup=2500; thin=1;
post-warmup draws per chain=2500, total post-warmup draws=10000.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
mu 2.55 0.00 0.06 2.45 2.52 2.55 2.59 2.66 6030 1
sigma 0.58 0.00 0.04 0.50 0.55 0.58 0.61 0.67 5432 1
lp__ -88.75 0.02 1.01 -91.50 -89.13 -88.44 -88.04 -87.77 3712 1
Samples were drawn using NUTS(diag_e) at Mon Feb 20 09:26:53 2023.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
We have 10,000 posterior distributions.
Get to know your data very well.